Efficient thermo‐mechanical model for solidification processes

A new, computationally efficient algorithm has been implemented to solve for thermal stresses, strains, and displacements in realistic solidification processes which involve highly nonlinear constitutive relations. A general form of the transient heat equation including latent‐heat from phase transformations such as solidification and other temperature‐dependent properties is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the highly nonlinear thermo‐elastic‐viscoplastic constitutive equations using a two‐level method. First, an estimate of the stress and inelastic strain is obtained at each local integration point by implicit integration followed by a bounded Newton–Raphson (NR) iteration of the constitutive law. Then, the global finite element equations describing the boundary value problem are solved using full NR iteration. The procedure has been implemented into the commercial package Abaqus (Abaqus Standard Users Manuals, v6.4, Abaqus Inc., 2004) using a user‐defined subroutine (UMAT) to integrate the constitutive equations at the local level. Two special treatments for treating the liquid/mushy zone with a fixed grid approach are presented and compared. The model is validated both with a semi‐analytical solution from Weiner and Boley (J. Mech. Phys. Solids 1963; 11:145–154) as well as with an in‐house finite element code CON2D (Metal. Mater. Trans. B 2004; 35B(6):1151–1172; Continuous Casting Consortium Website. http://ccc.me.uiuc.edu [30 October 2005]; Ph.D. Thesis, University of Illinois, 1993; Proceedings of the 76th Steelmaking Conference, ISS, vol. 76, 1993) specialized in thermo‐mechanical modelling of continuous casting. Both finite element codes are then applied to simulate temperature and stress development of a slice through the solidifying steel shell in a continuous casting mold under realistic operating conditions including a stress state of generalized plane strain and with actual temperature‐dependent properties. Other local integration methods as well as the explicit initial strain method used in CON2D for solving this problem are also briefly reviewed and compared. Copyright © 2006 John Wiley & Sons, Ltd.